Abstract : This paper explains the existence of a particular formal model drawn from Theoretical Astrophysics whose thermodyna-mical phenomenology shows a possible second order phase transition according to Landau-s Thermodynamical Theory that seems does not verify the Birman-Goldrich-Jari¢ chain subduction criterion and the Ascher-s maximality criterion of Landau-s Phenomenological Theory. Therefore, it follows that Landau-s Phenomenological Theory is more restrictive than the Landau-s Thermodynamical Theory.